Nucleon-quark mixed matter and neutron-star equation of state

The nucleon-quark mixed matter is defined in the Brueckner-Hartree-Fock framework, in which quark densities are determined by equilibrium conditions between nucleon and quark chemical potentials, and nucleon-quark interactions play critical roles for resulting equations of state (EoSs). The two models of EoSs are derived from the nucleon-quark mixed matter (NQMM): The NQMM-A EoSs are based on the simple assumption that nucleons and free quarks occupy their respective Fermi levels and their Fermi spheres overlap from each other. In NQMM-B EoSs, the quark Fermi repulsion effect is incorporated on the basis of quarkyonic matter, meaning that the nucleon Fermi levels are pushed up from the quark Fermi sphere by the Pauli exclusion principle. For the NQMM-A EoSs, the neutron-star mass-radius $\left(MR\right)$ curves are pushed up above the region of $M\sim 2.1M_{\odot }$ and $R_{2.1M_{\odot }}\sim 12.5$ km indicated by recent observations, as the $qN$ repulsions increase. For the NQMM-B EoSs, similar results are obtained by the combined contributions from the $qN$ repulsion and the quark Fermi repulsion. In both models of EoSs, the important roles of the $qN$ diquark exchange repulsions are demonstrated to reproduce reasonable values of $M_{\max }$ and $R_{2.1M_{\odot }}$.